How to compress URL parameters

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Say I have a single-page application that uses a third party API for content. The app’s logic is in-browser only, and there is no backend I can write to.

To allow de

Burrows-Wheeler+move-to-front+Huffman transform

I'm not quite sure BWT would be best suited for your kind of input.
This is no regular text, so recurring patterns would probably not occur as often as in source code or plain English.

Besides, a dynamic Huffman code would have to be passed along with the encoded data which, for very short input strings, would harm the compression gain badly.

I might well be wrong, in which case I would gladly see someone prove me to be.

Anyway, I decided to try another approach.

General principle

1) define a structure for your URL parameters and strip the constant part

for instance, starting from:

repos=aaa,bbb,ccc&
labels=ffffd,eee,fff&
milestones=ggg,hhh,iii&
username=kkk&
show_open=0&
show_closed=1&
show_commented=1&
show_uncommented=0

extract:

aaa,bbb,ccc|ffffd,eee,fff|ggg,hhh,iii|kkk|0110

where , and | act as string and/or field terminators, while boolean values don't need any.

2) define a static repartition of symbols based on the expected average input and derive a static Huffman code

Since transmitting a dynamic table would take more space than your initial string, I think the only way to achhieve any compression at all is to have a static huffman table.

However, you can use the structure of your data to your advantage to compute reasonable probabilities.

You can start with the repartition of letters in English or other languages and throw in a certain percentage of numbers and other punctuation signs.

Testing with a dynamic Huffman coding, I saw compression rates of 30 to 50%.

This means with a static table you can expect maybe a .6 compression factor (reducing the lenght of your data by 1/3), not much more.

3) convert this binary Huffmann code into something an URI can handle

The 70 regular ASCII 7 bits chars in that list

!'()*-.0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ_abcdefghijklmnopqrstuvwxyz

would give you an expansion factor of about 30%, practically no better than a base64 encode.

A 30% expansion would ruin the gain from a static Huffman compression, so this is hardly an option!

However, since you control the encoding client and server side, you can use about anything that is not an URI reserved character.

An interesting possiblity would be to complete the above set up to 256 with whatever unicode glyphs, which would allow to encode your binary data with the same number of URI-compliant characters, thus replacing a painful and slow bunch of long integer divisions with a lightning fast table lookup.

Structure description

The codec is meant to be used both client and server side, so it is essential that server and clients share a common data structure definition.

Since the interface is likely to evolve, it seems wise to store a version number for upward compatibility.

The interface definition will use a very minimalistic description language, like so:

v   1               // version number (between 0 and 63)
a   en              // alphabet used (English)
o   10              // 10% of digits and other punctuation characters
f   1               // 1% of uncompressed "foreign" characters
s 15:3 repos        // list of expeced 3 strings of average length 15
s 10:3 labels
s 8:3  milestones
s 10   username     // single string of average length 10
b      show_open    // boolean value
b      show_closed
b      show_commented
b      show_uncommented

Each language supported will have a frequency table for all its used letters

digits and other computerish symbols like -, . or _ will have a global frequency, regardless of languages

separators (, and |) frequencies will be computed according to the number of lists and fields present in the structure.

All other "foreign" characters will be escaped with a specific code and encoded as plain UTF-8.

Implementation

The bidirectional conversion path is as follows:

list of fields <-> UTF-8 data stream <-> huffman codes <-> URI

Here is the main codec

include ('class.huffman.codec.php');
class IRI_prm_codec
{
    // available characters for IRI translation
    static private $translator = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyzÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõöùúûüýþÿĀāĂăĄąĆćĈĉĊċČčĎďĐđĒēĔĕĖėĘęĚěĜĝĞğĠġĢģĤĥĦħĨĩĪīĬĭĮįİıĲĳĴĵĶķĸĹĺĻļĽľĿŀŁłŃńŅņŇňŉŊŋŌōŎŏŐőŒœŔŕŖŗŘřŚśŜŝŞşŠšŢţŤťŦŧŨũŪūŬŭŮůŰűŲųŴŵŶŷŸŹźŻżŽžſƀƁƂƃƄƅ";

    const VERSION_LEN = 6; // version number between 0 and 63

    // ========================================================================
    // constructs an encoder
    // ========================================================================
    public function __construct ($config)
    {
        $num_record_terminators = 0;
        $num_record_separators = 0;
        $num_text_sym = 0;

        // parse config file
        $lines = file($config, FILE_IGNORE_NEW_LINES|FILE_SKIP_EMPTY_LINES);
        foreach ($lines as $line)
        {
            list ($code, $val) = preg_split('/\s+/', $line, 2);
            switch ($code)
            {
            case 'v': $this->version = intval($val); break;
            case 'a': $alphabet = $val; break;
            case 'o': $percent_others = $val; break;
            case 'f': $percent_foreign = $val; break;
            case 'b':
                $this->type[$val] = 'b';
                break;
            case 's':
                list ($val, $field) = preg_split('/\s+/u', $val, 2);
                @list ($len,$num) = explode (':', $val);
                if (!$num) $num=1;
                $this->type[$field] = 's';
                $num_record_terminators++;
                $num_record_separators+=$num-1;
                $num_text_sym += $num*$len;
                break;

            default: throw new Exception ("Invalid config parameter $code");
            }
        }

        // compute symbol frequencies           
        $total = $num_record_terminators + $num_record_separators + $num_text_sym + 1;

        $num_chars = $num_text_sym * (100-($percent_others+$percent_foreign))/100;
        $num_sym = $num_text_sym * $percent_others/100;
        $num_foreign = $num_text_sym * $percent_foreign/100;

        $this->get_frequencies ($alphabet, $num_chars/$total);
        $this->set_frequencies (" .-_0123456789", $num_sym/$total);
        $this->set_frequencies ("|", $num_record_terminators/$total);
        $this->set_frequencies (",", $num_record_separators/$total);
        $this->set_frequencies ("\1", $num_foreign/$total);
        $this->set_frequencies ("\0", 1/$total);

        // create Huffman codec
        $this->huffman = new Huffman_codec();
        $this->huffman->make_code ($this->frequency);
    }

    // ------------------------------------------------------------------------
    // grab letter frequencies for a given language
    // ------------------------------------------------------------------------
    private function get_frequencies ($lang, $coef)
    {
        $coef /= 100;
        $frequs = file("$lang.dat", FILE_IGNORE_NEW_LINES|FILE_SKIP_EMPTY_LINES);
        foreach ($frequs as $line)
        {
            $vals = explode (" ", $line);
            $this->frequency[$vals[0]] = floatval ($vals[1]) * $coef;
        }
    }

    // ------------------------------------------------------------------------
    // set a given frequency for a group of symbols
    // ------------------------------------------------------------------------
    private function set_frequencies ($symbols, $coef)
    {
        $coef /= strlen ($symbols);
        for ($i = 0 ; $i != strlen($symbols) ; $i++) $this->frequency[$symbols[$i]] = $coef;
    }

    // ========================================================================
    // encodes a parameter block
    // ========================================================================
    public function encode($input)
    {
        // get back input values
        $bools = '';
        foreach (get_object_vars($input) as $prop => $val)
        {
            if (!isset ($this->type[$prop])) throw new Exception ("unknown property $prop");
            switch ($this->type[$prop])
            {
            case 'b': $bools .= $val ? '1' : '0'; break;
            case 's': $strings[] = $val; break;
            default: throw new Exception ("Uh oh... type ".$this->type[$prop]." not handled ?!?");
            }
        }

        // set version number and boolean values in front
        $prefix = sprintf ("%0".self::VERSION_LEN."b$bools", $this->version);

        // pass strings to our Huffman encoder
        $strings = implode ("|", $strings);
        $huff = $this->huffman->encode ($strings, $prefix, "UTF-8");

        // translate into IRI characters
        mb_internal_encoding("UTF-8");
        $res = '';
        for ($i = 0 ; $i != strlen($huff) ; $i++) $res .= mb_substr (self::$translator, ord($huff[$i]), 1);

        // done
        return $res;
    }

    // ========================================================================
    // decodes an IRI string into a lambda object
    // ========================================================================
    public function decode($input)
    {
        // convert IRI characters to binary
        mb_internal_encoding("UTF-8");
        $raw = '';
        $len = mb_strlen ($input);
        for ($i = 0 ; $i != $len ; $i++)
        {
            $c = mb_substr ($input, 0, 1);
            $input = mb_substr ($input, 1);
            $raw .= chr(mb_strpos (self::$translator, $c));
        }

        $this->bin = '';        

        // check version
        $version = $this->read_bits ($raw, self::VERSION_LEN);
        if ($version != $this->version) throw new Exception ("Version mismatch: expected {$this->version}, found $version");

        // read booleans
        foreach ($this->type as $field => $type)
            if ($type == 'b')
                $res->$field = $this->read_bits ($raw, 1) != 0;

        // decode strings
        $strings = explode ('|', $this->huffman->decode ($raw, $this->bin));
        $i = 0;
        foreach ($this->type as $field => $type) 
            if ($type == 's')
                $res->$field = $strings[$i++];

        // done
        return $res;
    }

    // ------------------------------------------------------------------------
    // reads raw bit blocks from a binary string
    // ------------------------------------------------------------------------
    private function read_bits (&$raw, $len)
    {
        while (strlen($this->bin) < $len)
        {
            if ($raw == '') throw new Exception ("premature end of input"); 
            $this->bin .= sprintf ("%08b", ord($raw[0]));
            $raw = substr($raw, 1);
        }
        $res = bindec (substr($this->bin, 0, $len));
        $this->bin = substr ($this->bin, $len);
        return $res;
    }
}

The underlying Huffman codec

include ('class.huffman.dict.php');

class Huffman_codec
{
    public  $dict = null;

    // ========================================================================
    // encodes a string in a given string encoding (default: UTF-8)
    // ========================================================================
    public function encode($input, $prefix='', $encoding="UTF-8")
    {
        mb_internal_encoding($encoding);
        $bin = $prefix;
        $res = '';
        $input .= "\0";
        $len = mb_strlen ($input);
        while ($len--)
        {
            // get next input character
            $c = mb_substr ($input, 0, 1);
            $input = substr($input, strlen($c)); // avoid playing Schlemiel the painter

            // check for foreign characters
            if (isset($this->dict->code[$c]))
            {
                // output huffman code
                $bin .= $this->dict->code[$c];
            }
            else // foreign character
            {
                // escape sequence
                $lc = strlen($c);
                $bin .= $this->dict->code["\1"] 
                     . sprintf("%02b", $lc-1); // character length (1 to 4)

                // output plain character
                for ($i=0 ; $i != $lc ; $i++) $bin .= sprintf("%08b", ord($c[$i]));
            }

            // convert code to binary
            while (strlen($bin) >= 8)
            {
                $res .= chr(bindec(substr ($bin, 0, 8)));
                $bin = substr($bin, 8);
            }
        }

        // output last byte if needed
        if (strlen($bin) > 0)
        {
            $bin .= str_repeat ('0', 8-strlen($bin));
            $res .= chr(bindec($bin));
        }

        // done
        return $res;
    }

    // ========================================================================
    // decodes a string (will be in the string encoding used during encoding)
    // ========================================================================
    public function decode($input, $prefix='')
    {
        $bin = $prefix;
        $res = '';
        $len = strlen($input);
        for ($i=0 ;;)
        {
            $c = $this->dict->symbol($bin);

            switch ((string)$c)
            {
            case "\0": // end of input
                break 2;

            case "\1": // plain character

                // get char byte size
                if (strlen($bin) < 2)
                {
                    if ($i == $len) throw new Exception ("incomplete escape sequence"); 
                    $bin .= sprintf ("%08b", ord($input[$i++]));
                }
                $lc = 1 + bindec(substr($bin,0,2));
                $bin = substr($bin,2);
                // get char bytes
                while ($lc--)
                {
                    if ($i == $len) throw new Exception ("incomplete escape sequence"); 
                    $bin .= sprintf ("%08b", ord($input[$i++]));
                    $res .= chr(bindec(substr($bin, 0, 8)));
                    $bin = substr ($bin, 8);
                }
                break;

            case null: // not enough bits do decode further

                // get more input
                if ($i == $len) throw new Exception ("no end of input mark found"); 
                $bin .= sprintf ("%08b", ord($input[$i++]));
                break;

            default:  // huffman encoded

                $res .= $c;
                break;          
            }
        }

        if (bindec ($bin) != 0) throw new Exception ("trailing bits in input");
        return $res;
    }

    // ========================================================================
    // builds a huffman code from an input string or frequency table
    // ========================================================================
    public function make_code ($input, $encoding="UTF-8")
    {
        if (is_string ($input))
        {
            // make dynamic table from the input message
            mb_internal_encoding($encoding);
            $frequency = array();
            while ($input != '')
            {
                $c = mb_substr ($input, 0, 1);
                $input = mb_substr ($input, 1);
                if (isset ($frequency[$c])) $frequency[$c]++; else $frequency[$c]=1;
            }
            $this->dict = new Huffman_dict ($frequency);
        }
        else // assume $input is an array of symbol-indexed frequencies
        {
            $this->dict = new Huffman_dict ($input);
        }
    }
}

And the huffman dictionary

class Huffman_dict
{
    public  $code = array();

    // ========================================================================
    // constructs a dictionnary from an array of frequencies indexed by symbols
    // ========================================================================
    public function __construct ($frequency = array())
    {
        // add terminator and escape symbols
        if (!isset ($frequency["\0"])) $frequency["\0"] = 1e-100;
        if (!isset ($frequency["\1"])) $frequency["\1"] = 1e-100;

        // sort symbols by increasing frequencies
        asort ($frequency);

        // create an initial array of (frequency, symbol) pairs
        foreach ($frequency as $symbol => $frequence) $occurences[] = array ($frequence, $symbol);

        while (count($occurences) > 1)
        {
            $leaf1 = array_shift($occurences);
            $leaf2 = array_shift($occurences);
            $occurences[] = array($leaf1[0] + $leaf2[0], array($leaf1, $leaf2));
            sort($occurences);
        }
        $this->tree = $this->build($occurences[0], '');

    }

    // -----------------------------------------------------------
    // recursive build of lookup tree and symbol[code] table
    // -----------------------------------------------------------
    private function build ($node, $prefix)
    {
        if (is_array($node[1]))
        {
            return array (
                '0' => $this->build ($node[1][0], $prefix.'0'),
                '1' => $this->build ($node[1][1], $prefix.'1'));
        }
        else
        {
            $this->code[$node[1]] = $prefix;
            return $node[1];
        }
    }

    // ===========================================================
    // extracts a symbol from a code stream
    // if found     : updates code stream and returns symbol
    // if not found : returns null and leave stream intact
    // ===========================================================
    public function symbol(&$code_stream)
    {
        list ($symbol, $code) = $this->get_symbol ($this->tree, $code_stream);
        if ($symbol !== null) $code_stream = $code;
        return $symbol;
    }

    // -----------------------------------------------------------
    // recursive search for a symbol from an huffman code
    // -----------------------------------------------------------
    private function get_symbol ($node, $code)
    {
        if (is_array($node))
        {
            if ($code == '') return null;
            return $this->get_symbol ($node[$code[0]], substr($code, 1));
        }
        return array ($node, $code);
    }
}

Example

include ('class.iriprm.codec.php');

$iri = new IRI_prm_codec ("config.txt");
foreach (array (
    'repos' => "discussion,documentation,hoodie-cli",
    'labels' => "enhancement,release-0.3.0,starter",
    'milestones' => "1.0.0,1.1.0,v0.7",
    'username' => "mklappstuhl",
    'show_open' => false,
    'show_closed' => true,
    'show_commented' => true,
    'show_uncommented' => false
) as $prop => $val) $iri_prm->$prop = $val;

$encoded = $iri->encode ($iri_prm);
echo "encoded as $encoded\n";
$decoded = $iri->decode ($encoded);
var_dump($decoded);

output:

encoded as 5ĶůťÊĕCOĔƀŪļŤłmĄZEÇŽÉįóšüÿjħũÅìÇēOĪäŖÏŅíŻÉĒQmìFOyäŖĞqæŠŹōÍĘÆŤŅËĦ

object(stdClass)#7 (8) {
  ["show_open"]=>
  bool(false)
  ["show_closed"]=>
  bool(true)
  ["show_commented"]=>
  bool(true)
  ["show_uncommented"]=>
  bool(false)
  ["repos"]=>
  string(35) "discussion,documentation,hoodie-cli"
  ["labels"]=>
  string(33) "enhancement,release-0.3.0,starter"
  ["milestones"]=>
  string(16) "1.0.0,1.1.0,v0.7"
  ["username"]=>
  string(11) "mklappstuhl"
}

In that example, the input got packed into 64 unicode characters, for an input length of about 100, yielding a 1/3 reduction.

An equivalent string:

discussion,documentation,hoodie-cli|enhancement,release-0.3.0,starter|
1.0.0,1.1.0,v0.7|mklappstuhl|0110

Would be compressed by a dynamic Huffman table to 59 characters. Not much of a difference.

No doubt smart data reordering would reduce that, but then you would need to pass the dynamic table along...

Chinese to the rescue?

Drawing on ttepasse's idea, one could take advantage of the huge number of Asian characters to find a range of 0x4000 (12 bits) contiguous values, to code 3 bytes into 2 CJK characters, like so:

    // translate into IRI characters
    $res = '';
    $len = strlen ($huff);
    for ($i = 0 ; $i != $len ; $i++)
    {
        $byte = ord($huff[$i]);
        $quartet[2*$i  ] = $byte >> 4;
        $quartet[2*$i+1] = $byte &0xF;
    }
    $len *= 2;
    while ($len%3 != 0) $quartet[$len++] = 0;
    $len /= 3;
    for ($i = 0 ; $i != $len ; $i++)
    {
        $utf16 = 0x4E00 // CJK page base, enough range for 2**12 (0x4000) values
               + ($quartet[3*$i+0] << 8)
               + ($quartet[3*$i+1] << 4)
               + ($quartet[3*$i+2] << 0);
        $c = chr ($utf16 >> 8) . chr ($utf16 & 0xFF);
        $res .= $c;
    }
    $res = mb_convert_encoding ($res, "UTF-8", "UTF-16");

and back:

    // convert IRI characters to binary
    $input = mb_convert_encoding ($input, "UTF-16", "UTF-8");
    $len = strlen ($input)/2;
    for ($i = 0 ; $i != $len ; $i++)
    {
        $val = (ord($input[2*$i  ]) << 8) + ord ($input[2*$i+1]) - 0x4E00;
        $quartet[3*$i+0] = ($val >> 8) &0xF;
        $quartet[3*$i+1] = ($val >> 4) &0xF;
        $quartet[3*$i+2] = ($val >> 0) &0xF;
    }
    $len *= 3;
    while ($len %2) $quartet[$len++] = 0;
    $len /= 2;
    $raw = '';
    for ($i = 0 ; $i != $len ; $i++)
    {
        $raw .= chr (($quartet[2*$i+0] << 4) + $quartet[2*$i+1]);
    }

The previous output of 64 Latin chars

5ĶůťÊĕCOĔƀŪļŤłmĄZEÇŽÉįóšüÿjħũÅìÇēOĪäŖÏŅíŻÉĒQmìFOyäŖĞqæŠŹōÍĘÆŤŅËĦ

would "shrink" to 42 Asian characters:

乙堽孴峴勀垧壩坸冫嚘佰嫚凲咩俇噱刵巋娜奾埵峼圔奌夑啝啯嶼勲婒婅凋凋伓傊厷侖咥匄冯塱僌

However, as you can see, the sheer bulk of your average ideogram makes the string actually longer (pixel-wise), so even if the idea was promising, the outcome is rather disappointing.

Picking thinner glyphs

On the other hand, you can try to pick "thin" characters as a base for URI encoding. For instance:

█ᑊᵄ′ӏᶟⱦᵋᵎiïᵃᶾ᛬ţᶫꞌᶩ᠇܂اlᶨᶾᛁ⁚ᵉʇȋʇίן᠙ۃῗᥣᵋĭꞌ៲ᛧ༚ƫܙ۔ˀȷˁʇʹĭ∕ٱ;łᶥյ;ᴶ⁚ĩi⁄ʈ█

instead of

█5ĶůťÊĕCOĔƀŪļŤłmĄZEÇŽÉįóšüÿjħũÅìÇēOĪäŖÏŅíŻÉĒQmìFOyäŖĞqæŠŹōÍĘÆŤŅËĦ█

That will shrink the length by half with proportional fonts, including in a browser address bar.

My best candidate set of 256 "thin" glyphs so far:

᠊།ᑊʲ་༌ᵎᵢᶤᶩᶪᶦᶧˡ ⁄∕เ'Ꞌꞌ꡶ᶥᵗᶵᶨ|¦ǀᴵ  ᐧᶠᶡ༴ˢᶳ⁏ᶴʳʴʵ։᛬⍮ʹ′ ⁚⁝ᵣ⍘༔⍿ᠵᥣᵋᵌᶟᴶǂˀˁˤ༑,.   ∙Ɩ៲᠙ᵉᵊᵓᶜᶝₑₔյⵏⵑ༝༎՛ᵞᵧᚽᛁᛂᛌᛍᛙᛧᶢᶾ৷⍳ɩΐίιϊᵼἰἱἲἳἴἵἶἷὶίῐῑῒΐῖῗ⎰⎱᠆ᶿ՝ᵟᶫᵃᵄᶻᶼₐ∫ª౹᠔/:;\ijltìíîïĩīĭįıĵĺļłţŧſƚƫƭǐǰȉȋțȴȷɉɨɪɫɬɭʇʈʝːˑ˸;·ϳіїјӏ᠇ᴉᵵᵻᶅᶖḭḯḷḹḻḽṫṭṯṱẗẛỉị⁞⎺⎻⎼⎽ⱡⱦ꞉༈ǁ‖༅༚ᵑᵝᵡᵦᵪา᠑⫶ᶞᚁᚆᚋᚐᚕᵒᵔᵕᶱₒⵗˣₓᶹๅʶˠ᛫ᵛᵥᶺᴊ

Conclusion

This implementation should be ported to JavaScript to allow client-server exchange.
You should also provide a way to share the structure and Huffman codes with the clients.

It is not difficult and rather fun to do, but that means even more work :).

The Huffman gain in term of characters is around 30%.

Of course these characters are multibyte for the most part, but if you aim for the shortest URI it does not matter.
Except for the booleans that can easily be packed to 1 bit, those pesky strings seem rather reluctant to be compressed.
It might be possible to better tune the frequencies, but I doubt you will get above 50% compression rate.

On the other hand, picking thin glyphs does actually more to shrink the string.

So all in all the combination of both might indeed achieve something, though it's a lot of work for a modest result.

0 讨论(0)

伪装坚强ぢ

2020-12-04 11:54

Why not use a third party link shortener?

(I am assuming you don't have a problem with URI length limits since you mentioned this is an existing application.)

It looks like you're writing a Greasemonkey script or thereabouts, so perhaps you have access to GM_xmlhttpRequest(), which would allow use of a third party link shortener.

Otherwise, you'd need to use XMLHttpRequest() and host your own link shortening service on the same server to avoid crossing the same-origin policy boundary. A quick online search for hosting your own shorteners supplied me with a list of 7 free/open source PHP link shortener scripts and one more on GitHub, though the question likely excludes this kind of approach since "The app’s logic is in-browser only, and there is no backend I can write to."

You can see example code implementing this kind of thing in the URL Shortener UserScript (for Greasemonkey), which pops up a shortened version of the current page's URL when you press SHIFT+T.

Of course, shorteners will redirect users to the long form URL, but this would be a problem in any non-server-side solution. At least a shortener can theoretically proxy (like Apache's RewriteRule with [P]) or use a <frame> tag.

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闹比i

2020-12-04 11:57

Just as you yourself propose, I would first get rid of all the characters that are not carrying any information, because they are part of the "format".

E.g. turn "labels=open,ssl,cypher&repository=275643&username=ryanbrg&milestones=&with_comment=yes" to "open,ssl,cyper|275643|ryanbrg||yes".

Then use a Huffmann encoding with a fixed probability vector (resulting in a fixed mapping from characters to variable length bitstrings - with the most probable characters mapped to shorter bitstrings and less probable characters mapped to longer bitstrings).

You could even use different probability vectors for the different parameters. For example in the parameter "labels" the alpha characters will have high probability, but in the "repository" parameter the numeric characters will have the highest probability. If you do this, you should consider the separator "|" a part of the preceeding parameter.

And finally turn the long bitstring (which is the concatenation all the bitstrings to which the characters were mapped) into something you can put into an URL by base64url encoding it.

If you could send me a set of representative parameter lists, I could run them through a Huffmann coder to see how well they compress.

The probability vector (or equivalently the mapping from characters to bitstrings) should be encoded as constant arrays into the Javascript function that is sent to the browser.

Of course you could go even further and - for example - try to get a list of possible lables with their probabilities. Then you could map entire lables to bitstrings with a Huffmann encoding. This will give you better compression, but you will have extra work for those labels that are new (e.g. falling back to the single character encoding), and of course the mapping (which - as mentioned above - is a constant array in the Javascript function) will be much larger.

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感情败类

2020-12-04 11:57

Small tip: Both parseInt and Number#toString support radix arguments. Try using a radix of 36 to encode numbers (or indexes into lists) in URLs.

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轻奢々

2020-12-04 11:58
I have a cunning plan! ^{(And a drink of gin tonic)}

You doesn't seem to care about the length of the bytestream but of the length of the resulting glyphs, e.g. what the string which is displayed to the user.

Browser are pretty good in converting an IRI to the underlying [URI][2] while still displaying the IRI in the address bar. IRIs have a greater repertoire of possible characters while your set of possible chars is rather limited.

That means you can encode bigrams of your chars (aa, ab, ac, …, zz & special chars) into one char of the full unicode spectrum. Say you've got 80 possible ASCII chars: the number of possible combinations of two chars is 6400. Which are easy findable in Unicodes assigned chars, e.g. in the han unified CJK spectrum:
```
aa  →  一
ab  →  丁
ac  →  丂
ad  →  七
…
```
I picked CJK because this is only (slighty) reasonable if the target chars are assigned in unicode and have assigned glyphs on the major browser and operating systems. For that reason the private use area is out and the more efficient version using trigrams (whose possible combinations could use all of Unicodes 1114112 possible code points) are out.

To recap: the underlying bytes are still there and – given UTF-8 encoding – possible even longer, but the string of displayed characters the user sees and copies is 50% shorter.

Ok, Ok, reasons, why this solution is insane:
- IRIs are not perfect. A lot of lesser tools than modern browser have their problems.
- The algorithm needs obviously a lot of more work. You'll need a function which maps the bigrams to the target chars and back. And it should preferable work arithmetically to avoid big hash tables in memory.
- The target chars should be checked if they are assigned and if they are simple chars and not fancy unicodian things like combining chars or stuff that got lost somewhere in Unicode normalization. Also if the target area is an continuous span of assigned chars with glyphs.
- Browser are sometimes wary of IRIs. For good reason, given the IDN homograph attacks. Are they OK with all these non-ASCII-chars in their address bar?
- And the biggest: people are notoriously bad at remembering characters in scripts they don't know. They are even worse at trying to (re)-type these chars. And copy'n'paste can go wrong in many different clicks. There is a reason URL shorteners use Base64 and even smaller alphabets.
… speaking of which: That would be my solution. Offloading the work of shortening links either to the user or integrating goo.gl or bit.ly via their APIs.
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